{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Introduction to Radar Using Python and MATLAB***\n",
    "## Andy Harrison - Copyright (C) 2019 Artech House\n",
    "<br/>\n",
    "\n",
    "# Probability Distributions\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability density function for a Gaussian distribution is given by \n",
    "\n",
    "\\begin{equation}\\label{eq:gaussian_pdf}\n",
    "    p(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right),\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mu$ is the mean and $\\sigma$ is the standard deviation. This probability density function may be calculated using the SciPy implementation ***scipy.stats.norm.pdf(x, loc, scale)***, where the keyword ***loc*** is the mean and keyword ***scale*** is the standard deviation.\n",
    "\n",
    "Other probability functions may be found from the routines in `scipy.stats` as shown in this example.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the location, scale and shape factor for the distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "loc = 2.0\n",
    "\n",
    "scale = 1.0\n",
    "\n",
    "shape_factor = 10.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the type of distribution (Gaussian, Weibull, Rayleigh, Rice or Chi-Squared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution_type = 'Gaussian'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the distributions from the `scipy` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm, weibull_min, rayleigh, rice, chi2\n",
    "\n",
    "from numpy import linspace\n",
    "\n",
    "\n",
    "if distribution_type == 'Gaussian':\n",
    "\n",
    "    x = linspace(norm.ppf(0.001, loc, scale),  norm.ppf(0.999, loc, scale), 200)\n",
    "\n",
    "    y = norm.pdf(x, loc, scale)\n",
    "\n",
    "elif distribution_type == 'Weibull':\n",
    "\n",
    "    x = linspace(weibull_min.ppf(0.001, shape_factor), weibull_min.ppf(0.999, shape_factor), 200)\n",
    "\n",
    "    y = weibull_min.pdf(x, shape_factor, loc, scale)\n",
    "\n",
    "elif distribution_type == 'Rayleigh':\n",
    "\n",
    "    x = linspace(rayleigh.ppf(0.001, loc, scale), rayleigh.ppf(0.999, loc, scale), 200)\n",
    "\n",
    "    y = rayleigh.pdf(x, loc, scale)\n",
    "\n",
    "elif distribution_type == 'Rice':\n",
    "\n",
    "    x = linspace(rice.ppf(0.001, shape_factor), rice.ppf(0.999, shape_factor), 200)\n",
    "\n",
    "    y = rice.pdf(x, shape_factor, loc, scale)\n",
    "\n",
    "elif distribution_type == 'Chi Squared':\n",
    "\n",
    "    x = linspace(chi2.ppf(0.001, shape_factor), chi2.ppf(0.999, shape_factor), 200)\n",
    "\n",
    "    y = chi2.pdf(x, shape_factor, loc, scale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the resulting probability distribution using the `matplotlib` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "# Set the figure size\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 10)\n",
    "\n",
    "\n",
    "\n",
    "# Display the results\n",
    "\n",
    "plt.plot(x, y, '')\n",
    "\n",
    "\n",
    "\n",
    "# Set the plot title and labels\n",
    "\n",
    "plt.title('Probability Density Function', size=14)\n",
    "\n",
    "plt.xlabel('x', size=12)\n",
    "\n",
    "plt.ylabel('Probability p(x)', size=12)\n",
    "\n",
    "\n",
    "\n",
    "# Set the tick label size\n",
    "\n",
    "plt.tick_params(labelsize=12)\n",
    "\n",
    "\n",
    "\n",
    "# Turn on the grid\n",
    "\n",
    "plt.grid(linestyle=':', linewidth=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
